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Question

# Tangents are drawn from different points on the line xâˆ’y+10=0 to the parabola y2=4x. If the chords of contact pass through a fixed point, then the coordinates of the fixed point is

A
(2,5)
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B
(5,2)
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C
(10,2)
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D
(2,10)
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Solution

## The correct option is C (10,2)Let any point on the line x−y+10=0 be (t,t+10) From this point, the equation of chord of contact to the parabola y2=4x is, T=0 ⇒y(t+10)=2(x+t) ⇒2x−10y+t(2−y)=0 So, the fixed point is the intersection of line, ⇒2x−10y=0 & 2−y=0 ⇒y=2⇒x=10 Hence, the fixed point is (10,2)

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